Answer:
[tex]56 \text{ cm}^2/\text{s}[/tex]
Explanation:
This question is about the rate of change of the square's area, which can be solved using differentiation.
Let the side of the square be S while the area of the square be A.
Given: [tex]\frac{dS}{dt} =7[/tex]cm/s
Find: [tex]\frac{dA}{dt}[/tex], when A= 16 cm²
Start by writing A in terms of S and differentiate A with respect to S.
A= S×S= [tex]S^{2}[/tex]
[tex]\frac{dA}{dS}=2S[/tex]
Find the value of S when the area of the square is 16 [tex]\text{cm}^2[/tex].
When A= 16,
S²=16
S= ± √16
S= 4 or S= -4 (reject)
[tex]\frac{dA}{dt}=\frac{dA}{dS} \times\frac{dS}{dt}[/tex]
[tex]\frac{dA}{dt}[/tex]
= 2s ×7
= 14s
= 14(4)
= 56 cm²/s
Thus, the area of the square is increasing at a rate of 56 [tex]\bf{\text{cm}^2}[/tex]/s.
Additional:
For a similar question on rate of change, do check out the following!
